A characteristic number of Hamiltonian bundles over S2

JOURNAL OF GEOMETRY AND PHYSICS

卷:56

Article

Vina, Andres

关键词: Hamiltonian diffeomorphisms;    symplectic fibrations;   

DOI  :  10.1016/j.geomphys.2005.12.004

来源: Elsevier

【 摘 要 】

Each loop psi in the group Ham(M) of Hamiltonian diffeomorphisms of a symplectic manifold M determines a fibration E on S-2, whose coupling class [V. Guillemin, L. Lerman, S. Sternberg, Symplectic Fibrations and Multiplicity Diagrams, Cambridge U.P., Cambridge, 1996] is denoted by c. If VTE is the vertical tangent bundle of E, we relate the characteristic number integral(E)c(1)(VTE)c(n) to the Maslov index of the linearized flow psi t(*) and the Chern class c(1) (TM). We give the value of this characteristic number for loops of Hamiltonian symplectomorphisms of Hirzebruch surfaces. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

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